Unfortunately, hot glue is perhaps your best alternative, you just have to be patient with it (and make sure you're wearing a good pair of gloves). Unlike cements or other adhesives, hot glue doesn't adhere instantaneously, you have to hold the pieces together firmly and give the glue a chance to bond, which
does take a few minutes, and your fingers and thumbs
do get tired, but that's how hot glue works.
I'm not sure if spray adhesive could be used as an alternative, I've never tried it on foam before, but similar to contact, you spray it first, give it at least a minute to get tacky, then press the pieces together so they'll bond. But again, this is usually for attaching things like eyes or other features, and again, I haven't tried it on foam rubber, so I don't know how that would hold up.
If you were ever willing to invest in a good respirator, like this one I ordered from Walmart a couple of years ago (link:
https://www.walmart.com/ip/3M-6300-Large-6000-Series-Facepiece-Respirator-Half-Mask/21779006), with the right kind of cartridges for breathing, I think you would enjoy working with the contact, because it's amazing: rather than spending you time gluing and holding, gluing and holding, you could start applying the contact to the foam, then move onto other pieces, then depending on how many other pieces you have to apply the contact to, it could be time to already go back and start pressing the older pieces together to stick (it usually takes about 15 minutes for the contact to dry).